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Netlib. Some good ones:

* LAPACK (BLAS is there too) http://www.netlib.org/lapack/explore-html/

* QUADPACK (quadrature integration) http://www.netlib.org/quadpack/

* MINPACK (nonlinear solvers) http://netlib.org/minpack/index.html

* ODEPACK (ordinary differential equations) http://netlib.org/odepack/index.html

Most of the textbooks on numerical methods are not very approachable, but Carl Meyer's Matrix Analysis and Applied Linear Algebra text is a good start, as are Gilbert Strang's books.

Note that SciPy wraps all of these in nice Python wrappers. (That's basically its reason for being.)

Try the Fortran Wiki

http://fortranwiki.org/fortran/show/Libraries

There are a few places that use FORTRAN extensively. The two I am aware of being Weather simulations and ESDU[1].

[1] https://www.esdu.com/cgi-bin/ps.pl?sess=unlicensed_117111319...

Hairer's DOP853 is a differential equations solver that a lot of people seem to be enamored with:

http://www.unige.ch/~hairer/prog/nonstiff/dop853.f

In this case someone took the old fortran code and modernized it a bit, yet again in fortran:

https://github.com/jacobwilliams/dop853